Math, asked by arzain11082018, 5 months ago

If sin A=3/4
calculate cos A and tan A.​

Answers

Answered by puttaadarsh9539
0

Step-by-step explanation:

5/4

3/5...................

Answered by Anonymous
3

 \huge \sf Answer :

 \sf cosA = \dfrac{\sqrt{7}}{4}

 \sf tanA = \dfrac{3}{\sqrt{7}}

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 \huge \sf Solution :

We know that,

 \sf sin \theta = \dfrac{Perpendicular}{Hypotenuse}

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According to Statement,

 \sf sin \theta = \dfrac{3}{4}

 \sf \implies \dfrac{Perpendicular}{Hypotenuse} = \dfrac{3}{4}

∴ Perpendicular for θ = 3x

and the hypotenuse for θ = 4x

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By Pythagoras' Theorem,

Hypotenuse² = Perpendicular² + Base²

 \sf⇒ AC² = AB² + BC²

 \sf⇒ (4x)² = (3x)² + BC²

 \sf⇒ 16x² = 9x² + BC²

 \sf⇒ 16x² - 9x² = BC²

 \sf⇒ 7x² = BC²

 \sf⇒ \sqrt{7x^{2}} = BC

 \sf⇒ BC = \sqrt{7}x

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Now, We have cosA and tanA will be,

 \sf cosA = \dfrac{Base}{Hypotenuse}

 \sf⇒ cosA = \dfrac{\sqrt{7}x}{4x}

 \sf⇒ cosA = \dfrac{\sqrt{7}}{4}

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 \sf tanA = \dfrac{Perpendicular}{Base}

 \sf⇒ tanA = \dfrac{3x}{\sqrt{7}x}

 \sf⇒ tanA = \dfrac{3}{\sqrt{7}}

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